Almost Sure Convergence of the Numerical Discretization of Stochastic Jump Diffusions

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)225-244
Journal / PublicationActa Applicandae Mathematicae
Issue number3
Publication statusPublished - 2000


Based on the shuffle product expansion of exponential Lie series in terms of a Philip Hall basis for the stochastic differential equations of jump-diffusion type, we can establish Stratonovich-Taylor-Hall (STH) schemes. However, the STHr scheme converges only at order r in the meansquare sense. In order to have the almost sure Stratonovich-Taylor-Hall (ASTH) schemes, we have to include all the terms related to multiple Poissonian integrals as the moments of multiple Poissonian integrals always have lower orders of magnitudes as compared with those of multiple Brownian integrals.

Research Area(s)

  • Almost sure convergence, Exponential Lie series, Jump diffusion, Philip Hall basis, Shuffle product, Stratonovich-Taylor expansion